Trying to JB old 3GS running iOS 4.0

I have an old 3GS that currently has iOS 4.0 installed. I've done some searching but couldn't determine the how I should proceed. I was wondering what would be the best way to JB this phone? Should I JB 4.0? Or update to 5.0.1 and then JB tethered? (tried to update phone to 4.3.3 and then jailbreak untethered, but I suppose this isn't possible since Apple isn't signing that version of ios anymore. Just thought I would get some advice from those who know tons more than me on this topic. Any help would be appreciated!